Chapter 9, Problem 65SGR

To determine

To find: an equation for the function which describes the given data.

Answer to Problem 65SGR

Linear equation

  $y=-3x+8$

Explanation of Solution

Given information :

$x$	0	1	2	3	4
$y$	8	5	2	-1	-4

Formula used : General equation of straight line of the form $y=mx+c$

Calculation : By subtracting the first value of $y$ from second value, then second value from third value, then third value from fourth value and so on. If the value is constant then linear equation displays the data.

  $5-8=-3$

  $2-5=-3$

  $-1-2=-3$

  $-4+1=-3$

Given model of the form $y=mx+c$ where $m$ is slope and $c$ is the $y-$ intercept

Difference $=-3=m$

  $y-$ Intercept is $\left(0,8\right)$ because $c=8$

Substituting value of $m$ and $c$ in $y=mx+c$

Equation is $y=-3x+8$